Fig. 6: Cost function value and fidelity versus number of iterations.

We implement VQSE for error mitigation of the three qubit W-state preparation circuit. The input state ρ corresponds to the mixed state obtained by running the W-state preparation circuit on a noisy simulator. The dashed line corresponds to the fidelity \(F(\rho ,\left|\psi \right\rangle )\) between ρ and the the exact W state \(\left|\psi \right\rangle\). For each iteration step, we compute the fidelity \(F(\sigma ,\left|\psi \right\rangle )\), where the mixed state σ is obtained by running the VQSE eigenvector preparation circuit on the noisy simulator. Curves depict the average of 10 instances of the algorithm. As the number of iterations increases the cost function value decreases, which implies that we are able to train V(θ) in the presence of noise. After a few iterations of the VQSE optimization loop, we find \(F(\sigma ,\left|\psi \right\rangle ) \,>\, F(\rho ,\left|\psi \right\rangle )\).